{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian regression analysis in lmfit\n",
    "In this example we will perform a Bayesian regression analysis in the `lmfit` package. You'll need the `emcee` and `corner` packages installed. Both of these are available on PyPI. We start off with the requisite imports."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import lmfit\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets create the data we'll then fit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1095b1d68>]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1StIta9QCiJN+udQjPINUWQwgbdp1AIwx9Db7MDCZlplEM/EAxpMmsrkCAoYm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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10954b0b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(1, 10, 250)\n",
    "np.random.seed(0)\n",
    "y = 3.0 * np.exp(-x / 2) - 5.0 * np.exp(-(x - 0.1) / 10.) + 0.1 * np.random.randn(len(x))\n",
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll need a `Parameters` object to store the Parameters of our model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "p = lmfit.Parameters()\n",
    "p.add_many(('a1', 4), ('a2', 4), ('t1', 3), ('t2', 3., True))\n",
    "\n",
    "def residual(p):\n",
    "    v = p.valuesdict()\n",
    "    return v['a1'] * np.exp(-x / v['t1']) + v['a2'] * np.exp(-(x - 0.1) / v['t2']) - y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll do a straightforward least-squares fit first, using the *Nelder-Mead* method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[Variables]]\n",
      "    a1:   2.98623688 (init= 4)\n",
      "    a2:  -4.33525596 (init= 4)\n",
      "    t1:   1.30993185 (init= 3)\n",
      "    t2:   11.8240752 (init= 3)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/andrew/miniconda3/envs/dev3/lib/python3.5/site-packages/ipykernel/__main__.py:6: RuntimeWarning: overflow encountered in exp\n",
      "/Users/andrew/miniconda3/envs/dev3/lib/python3.5/site-packages/ipykernel/__main__.py:6: RuntimeWarning: overflow encountered in multiply\n",
      "/Users/andrew/miniconda3/envs/dev3/lib/python3.5/site-packages/lmfit/minimizer.py:155: RuntimeWarning: overflow encountered in multiply\n",
      "  return (r*r).sum()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1095aa860>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Oq5me+U5DeVOv0deTu4FwlJx4InZgcRb7rJzHnicfwX5li5l550O8dePDNNjd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\n7dVeqm21otYDLhVR1Mpti4faAlpAQFEQSNjCErJ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RYk2G3HBr101LHCWx7UC1+/2cYHV7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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1095b1ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mi = lmfit.minimize(residual, p, method='Nelder', nan_policy='omit')\n",
    "lmfit.printfuncs.report_fit(mi.params, min_correl=0.5)\n",
    "plt.plot(x, y)\n",
    "plt.plot(x, residual(mi.params) + y, 'r')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The above analysis ignored the uncertainty on each datapoint. So we'll add in a noise Parameter to address that. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# add a noise parameter\n",
    "mi.params.add('noise', value=1, min=0.001, max=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the Bayesian analysis we have to calculate the log-posterior probability for the system. The log-posterior probability is the sum of the log-prior and log-likelihood probabilities. \n",
    "\n",
    "The log-prior encodes prior beliefs about the system. With the `lmfit.emcee` method the log-prior probability is assumed to be 0 if a `Parameter` is within its bounds. If it's outside the bounds the log-prior probability is `-np.inf`, i.e. impossible. This is known as a uniform prior.\n",
    "\n",
    "The log-likelihood function is the probability of the data given the model. The following function calculates the log-likelihood. Note how the [data uncertainties (http://dan.iel.fm/emcee/current/user/line/) are included in the log-likelihood.\n",
    "\n",
    "Note, if you want a non-uniform prior, then you should include the log-prior and log-likelihood in a single function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# This is the log-likelihood probability for the sampling. We're going to estimate the\n",
    "# size of the uncertainties on the data as well.\n",
    "def lnprob(p):\n",
    "    noise = p['noise']\n",
    "    return -0.5 * np.sum((residual(p) / noise)**2 + np.log(2 * np.pi * noise**2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With `lmfit.emcee` we first have to create a `lmfit.Minimizer` object. We're going to initialise it with the best fit from above.\n",
    "\n",
    "Then we do the sampling. We are going to burn in (discard) the first 300 steps out of a total of 1000. We are then going to thin, which reduces the amount of autocorrelation in the chain. Thinning by 20 means that 1 in 20 samples is kept."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/andrew/miniconda3/envs/dev3/lib/python3.5/site-packages/ipykernel/__main__.py:5: RuntimeWarning: overflow encountered in square\n",
      "/Users/andrew/miniconda3/envs/dev3/lib/python3.5/site-packages/ipykernel/__main__.py:6: RuntimeWarning: overflow encountered in exp\n",
      "/Users/andrew/miniconda3/envs/dev3/lib/python3.5/site-packages/ipykernel/__main__.py:6: RuntimeWarning: overflow encountered in multiply\n",
      "/Users/andrew/miniconda3/envs/dev3/lib/python3.5/site-packages/ipykernel/__main__.py:5: RuntimeWarning: overflow encountered in true_divide\n"
     ]
    }
   ],
   "source": [
    "mini = lmfit.Minimizer(lnprob, mi.params)\n",
    "res = mini.emcee(burn=300, steps=1000, thin=20, params=mi.params)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now lets plot the outcome with the `corner` package. Note the banana shapes, they arise out of non-normality for the parameter probability distribution. The elliptical nature of several parameter pairs indicates a high degree of correlation. The correlation parameter is returned as an attribute of the `res` OptimizeResult."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING:root:Too few points to create valid contours\n",
      "WARNING:root:Too few points to create valid contours\n"
     ]
    },
    {
     "data": {
      "image/png": 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ZZ2ru3LkyxigYDBZMLxtqtMadljawBbYrGAxut3scAAAAMF6NqYCj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\ngUAgvSBzai2y/ZVMJ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dasWYM+V+1LDoTb7SYajeL1evF6vUSje+TOg7ataDRKXl5e+jU5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mBn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\ne58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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1095bb908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import corner\n",
    "a=corner.corner(res.flatchain, labels=res.var_names, truths=list(res.params.valuesdict().values()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the output parameters, the correlations are also worked out. The `OptimizeResult` contains `chain` and `lnprob` attributes which contain the samples and corresponding log-probability. In addition, the Minimizer will then also contain a `sampler` attribute (a `emcee.EnsembleSampler` object) which can be used for other purposes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "median of posterior probability distribution\n",
      "------------------------------------------\n",
      "[[Variables]]\n",
      "    a1:      2.99174361 +/- 0.154968 (5.18%) (init= 2.986237)\n",
      "    a2:     -4.34900932 +/- 0.126443 (2.91%) (init=-4.335256)\n",
      "    t1:      1.32560305 +/- 0.145840 (11.00%) (init= 1.309932)\n",
      "    t2:      11.7790804 +/- 0.491648 (4.17%) (init= 11.82408)\n",
      "    noise:   0.09799658 +/- 0.004448 (4.54%) (init= 1)\n",
      "[[Correlations]] (unreported correlations are <  0.100)\n",
      "    C(a2, t1)                    = -0.945 \n",
      "    C(t2, noise)                 =  0.867 \n",
      "    C(a2, t2)                    =  0.851 \n",
      "    C(t1, t2)                    = -0.739 \n",
      "    C(a1, t1)                    = -0.688 \n",
      "    C(a1, t2)                    =  0.679 \n",
      "    C(a1, noise)                 =  0.618 \n",
      "    C(a2, noise)                 =  0.577 \n",
      "    C(a1, a2)                    =  0.560 \n",
      "    C(t1, noise)                 = -0.465 \n",
      "\n",
      "Maximum likelihood Estimation\n",
      "-----------------------------\n",
      "Parameters([('a1', <Parameter 'a1', 2.94177146455154, bounds=[-inf:inf]>), ('a2', <Parameter 'a2', -4.3479774858121809, bounds=[-inf:inf]>), ('t1', <Parameter 't1', 1.3357882186609258, bounds=[-inf:inf]>), ('t2', <Parameter 't2', 11.790528448102789, bounds=[-inf:inf]>)])\n"
     ]
    }
   ],
   "source": [
    "print(\"median of posterior probability distribution\")\n",
    "print('------------------------------------------')\n",
    "lmfit.report_fit(res.params)\n",
    "# find the maximum likelihood solution\n",
    "highest_prob = np.argmax(res.lnprob)\n",
    "hp_loc = np.unravel_index(highest_prob, res.lnprob.shape)\n",
    "mle_soln = res.chain[hp_loc]\n",
    "for i, par in enumerate(p):\n",
    "    p[par].value = mle_soln[i]\n",
    "print(\"\\nMaximum likelihood Estimation\")\n",
    "print('-----------------------------')\n",
    "print(p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10b660a58>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1Rx/NiuJiRpx8MjsqtN680yf0jtnE5Yyq1/PpTccwPdyOUdFymrUAhBCLgA5x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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b378ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)\n",
    "plt.plot(x, residual(mi.params) + y, 'r', label='Nelder-Mead')\n",
    "plt.plot(x, residual(res.params) + y, 'black', label='emcee')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, let's calculate some uncertainty intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 sigma spread 0.146560915084\n",
      "2 sigma spread 0.301737207291\n"
     ]
    }
   ],
   "source": [
    "quantiles = np.percentile(res.flatchain['t1'], [2.28, 15.9, 50, 84.2, 97.7])\n",
    "print(\"1 sigma spread\", 0.5 * (quantiles[3] - quantiles[1]))\n",
    "print(\"2 sigma spread\", 0.5 * (quantiles[4] - quantiles[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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